Ergodic Theory Workshop

作为我们在2002年6月、2003年2月、2004年和2005年成功举办的研讨会的延续，我们计划在2006年2月和2007年2月在北卡罗来纳大学教堂山分校数学系举办两次遍历式（和概率）研讨会。这些研讨会部分由伯克利数学科学研究所资助，是MSRI网络会议的一部分。他们也得到了北卡罗来纳大学教堂山分校数学系的部分支持。这些研讨会的主题是遍历平均收敛的最新进展及其与数论和概率论的联系。两个可能的主题是L1中遍历平均沿正方形的逐点收敛，以及最近显示的素数之间任意长等差数列的存在。该组织与过去的研讨会类似。在为期三天的研讨会中，我们试图将年轻的（研究生、博士后、助理教授）和高级研究人员聚集在一起。高级研究人员被要求做半说明性的演讲，让初级研究人员对一些活跃的研究领域有一个很好的介绍。鼓励年轻的研究人员，特别是博士生发表演讲和提出问题。在研讨会期间提出和讨论问题。就智力价值而言，2006年和2007年的研讨会为年轻的研究人员提供了一个机会，与遍历理论和相关领域的全球专家会面，并进行有益的讨论，这将促进他们的职业发展。年轻的研究人员将能够直接从会议网站申请旅行支持。高级研究人员当然会与他们的数学家同行进行富有成果的交流。就更广泛的影响而言，受邀演讲者的地位增加了整个数学系的知名度。来自代表性不足群体的数学家正在通过HBCU或AARMS网站的广告寻找，其中一些人被邀请发言。我们希望这样的研讨会将有助于增加来自代表性不足群体的数学家参与北卡罗来纳大学教堂山分校的研究生课程。与之前的研讨会一样，我们希望这些2006-2007年研讨会的论文集能在《当代数学》杂志上发表。第一次会议的标题是“教堂山遍历理论研讨会”。

ABSTRACTAs a continuation of the successful workshops we organized on June 2002, February 2003, 2004 and 2005, we are planning two ergodic (and probability) workshops in February 2006 and 2007 in the Department of Mathematics at the University of North Carolina at Chapel Hill. These workshops are partially funded by the Mathematical Sciences Research Institute at Berkeley and are part of the MSRI network conferences.They are also supported in part by the Department of Mathematics at UNC Chapel Hill.The main themes of these workshops are recent progress on the convergence of the ergodic averages and their connections with number theory and probability. Two possible topics could be the pointwise convergence of ergodic averages along the squares in L1 and the recently shown existence of arbitrary long arithmetic progressions among prime numbers. The organization is similar to the one used in the past workshops. We are trying to bring together young (graduate students, Post Doc, Assistant Professors) and senior researchers during the three days of the workshops. Senior researchers are asked to give semi expository talks to allow junior researchers to get a good introduction to some active research areas. Younger researchers and especially PhD students are encouraged to give talks and ask questions. Problems sessions are presented and discussed during the workshops. In terms of intellectual merit these 2006 and 2007 workshops provide an opportunity for young researchers to meet worldwide experts in ergodic theory and related fields and to have helpful discussions that would advance their career. Younger researchers will be able to apply for travel support directly from the conferences websites. Senior researchers certainly have fruitful exchanges with their fellow mathematicians. In terms of broader impact the standing of the invited speakers adds visibility to the Department of Mathematics as a whole. Mathematicians from under-represented groups are being looked for through advertisements at HBCU or the AARMS web sites and some are invited to speak. We hope that such workshops will help increase the participation of mathematicians from under represented groups into the graduate program at UNC Chapel Hill. As was the case with the previous workshops, we expect the proceedings of these 2006-2007 workshops to be published by Contemporary Mathematics. The first proceedings have appeared under the title "Chapel Hill ergodic theory workshops".